NavList:

Frank wrote

The earliest references I have found for the expression "cocked hat" referring to three crossing lines of position date from 1908-1910. Two describe problems in piloting or hydrographic surveying. A third reference was in Blackburne's tables and this one directly addressed astronomical lines of position, but this was at a point where he was quoting and then critiquing another author's book on "Sumner's Method" (which at this point in time reasonably meant any method for producing a celestial line of position). Because this feels like a later addition to the work, it may not date from 1908. In all of these the expression "cocked hat" is used without explanation. To me, this suggests that the metaphoric expression rose up from practitioners and was already popular before it appeared in print. So I would go with c.1900 as the origin of the metaphor.

Several references I have found, the earliest from the Amiralty Manual of Navigation 1922, use a pharase similar to   [a small triangle or "cocked hat"]. To me what is important is that cocked hat is in quotes which suggests that in the late 19th and early 20th century it was a slang expression.

A 1967 book on air navigation includes the quotes.  When were the quotes removed and "cocked hat" was no longerrt a slang word? Did professional navigators ever use the quote-less version or is it just post-gps enthusiasts who do?

I have glanced quickly through several volumes of Nicholls's and have not found any referenct to cocked hat. But it was a quick look and I may have missed it.